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arXiv · 2507.08252

Witnessing nonlocality in quantum network of continuous-variable systems by generalized quasiprobability functions

Taotao Yan·Jinchuan Hou·Xiaofei Qi·Kan He
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Abstract

Gaussian measurements can not be used to witness nonlocality in Gaussian states as well as the network nonlocality in networks of continuous-variable (CV) systems. Thus special non-Gaussian measurements have to be utilized. In the present paper, we first propose a kind of nonlinear Bell-type inequality that is applicable to quantum networks of both finite or infinite dimensional systems. Violation of the inequality will witness the network nonlocality. This inequality allows us to propose a method of the supremum strategy for detecting network nonlocality in CV systems with source states being any multipartite multi-mode Gaussian states according to the configurations of the networks by utilizing non-Gaussian measurements based on generalized quasiprobability functions. The nonlinear Bell-type inequalities for CV networks, which depend solely on the generalized quasiprobability functions of Gaussian states, are straightforward to construct and implement. As illustrations, we propose the corresponding nonlinear Bell-type inequalities for any chain, star, tree-shaped and cyclic networks in CV systems with source states being $(1+1)$-mode Gaussian states. The examples show that this approach works well for witnessing the nonlocality in networks of CV systems. Particularly, a thorough discussion is given for the entanglement swapping network. Our study provide a strong signature for the network nonlocality nature of CV systems and lead to precise recipes for its experimental verification.

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Taotao Yan, Jinchuan Hou, Xiaofei Qi, Kan He. 2025-07-17. Witnessing nonlocality in quantum network of continuous-variable systems by generalized quasiprobability functions. https://doi.org/10.1007/s11432-025-4753-8

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